Use Cases of Machine Learning in Queueing Theory Based on a GI/G/K System

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This article primarily explores the application of machine learning in queueing theory, particularly focusing on the role of supervised learning and reinforcement learning algorithms in assessing and optimizing the performance of queuing systems. After reading this article, I have the following questions:

1.      If the system is stable, i.e., ρ < 1, what do the conditions 0 < ρ < 0.95 and ρ ≥ 0.95 imply in specific terms?

2.      Why can it be observed from Table 1 that machine learning algorithms produce better estimates of data where there are not too large outliers?

3.      In Figure 13, what do the blue, green, and red regions represent respectively? And how are ρ=0.5, ρ=0.95, and ρ=0.3 depicted in the figure?

4.      What were the rationales behind selecting six models, such as Nearest Neighbors, for Table 1 and nine models, including Logistic Regression, for Table 4? How did you approach the model selection process? Was the decision influenced by their prevalence in the field?

5.      What were the specific reasons for selecting Logistic Regression and Neural Network models for comparing their performance characteristics in Table 2? Do these models possess any distinctive features? Why it can be thought that ‘the two algorithms give the best results’?

6.      “In unsupervised learning, we are given only the input data and the task is to find any patterns in these data in the absence of known values of the target function.” The phrasing of this sentence is not smooth, and it is advisable to restructure it for a more coherent and articulate presentation.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

 The English could be improved to more clearly express the research.

Author Response

The point-by-point response can be found in the separate file.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

1. The paper is an in-depth examination of the use of machine learning (ML) techniques in queueing theory with special focus on the GI/G/K queueing model. Though the effort to merge ML with conventional queueing models is laudable, the paper is unclear, technically erroneous, and directionless. It needs extreme revisions before it can be published.

 

2. Although the manuscript brings out a variety of applications of machine learning to queueing theory, the novelty is not highlighted properly. Some of the claims duplicate current research, e.g., those pertaining to phase-type distribution-based approximations and reinforcement learning, without adding significantly new. It is essential to state the new features of this research explicitly in relation to the referenced literature.

 

3. The paper lacks good flow. Though the sections are filled with technical details, they fail to create a clear link between them. Important points such as the reasons behind applying specific machine learning techniques are submerged in long descriptions. The sections need to be rewritten to facilitate logical flow, emphasizing the problem statement, methodology, results, and implications.

 

4. The use of PH approximations is not critically assessed. For example, PH distributions are suboptimal for heavy-tailed data, but they are not justified in such cases.

 

5. Mention alternative approaches (e.g., mixture distributions or empirical distributions) and why PH approximations are nevertheless preferred in spite of known shortcomings.

 

6. Simulation methods (event-driven vs. departure time) are explained in excellent detail, but it is not apparent how to determine which one to utilize in particular situations.

 

7. How would the models behave with real data that does not have clean distributions or does not meet PH fitting criteria?

 

8. Performance metrics (e.g., R², MSE) indicate abrupt performance degradation under heavy load conditions. The paper does not, however, offer practical ways of remedying this. Propose further preprocessing or sampling methods for coping with extreme data points, e.g., over-sampling high-load ranges.

 

9. In light of the inefficiencies observed above ρ > 0.9, how is this strategy implemented in practice in heavily loaded systems?

 

10. Overuse of mathematical equations and simulation details without contextual descriptions around them makes the paper difficult to read. Supplement technical sections with intuitive explanations or graphics. For instance, explain the simulation algorithms with diagrams.

 

11. Validation is primarily based on comparisons of simulation outputs with approximations, which do not reflect real-world variability or noise. Validate the ML models with empirical data or heterogeneous queueing systems to prove robustness.

 

12. How would the suggested approaches provide reliability under queuing systems that exhibit behavior outside typical GI/G/K limits, e.g., with highly correlated arrivals?

 

13. What is the computational tradeoff for utilizing PH distributions and other parametric fitting approaches for their scalability vs. accuracy?

 

14. How would the suggested reinforcement learning approaches handle environments with incomplete or uninterrupted data?

 

15. While the manuscript is dealing with a relevant problem, it needs to be greatly improved in terms of focus, clarity, and technicality. Improvement in originality and overcoming the evaluation, validation, and presentation issues is necessary for its acceptance.

 

Author Response

A point-to-point response can be found in the separate file.

Author Response File: Author Response.docx